Let me start by saying, I don't want to start any debate either, but just want to give some information/background from the standpoint of a medical person and from things I heard about how the refrigerator use at WDW works.
If you go to the website of almost any insulin manufacturer or look in the medication package insert for the insulin, you will find it says insulin for long term storage has to be kept in the refrigerator, but the bottle in use may be kept at room temperature and used within 28 days. The package insert provided by the manufacturer is their recommendations for storage. For whatever reason, your doctor may recommend something else that you follow, but whatever is recommended by the maker of the medication for storage is safe. (I'm not saying not to do what the doctor recommends for storage, just that the manufacturer's instructions for safe storage may be different than what the doctor says. This will be important further down the page).
The pharmacy puts a "Keep Refrigerated" sticker on it because bottles being kept for long term storage do need refrigeration per the manufacturer.
Now, with that as background, many years ago, Disney used to provide refrigerators for medication. One of the usual medications was insulin and many diabetics at that time were taught to keep all their insulin refrigerated. Now many diabetics are taught that the insulin in use is fine to be kept at room temperature and only long term storage insulin needs refrigeration.
When word got out that Disney was providing refrigerators at no cost for medical reasons, many people who did not have a medical reason were saying they did and requesting one. At that point, Disney elected for a while not to provide refrigerators free of charge to anyone. That proved to be very unpopular, so they looked at other ways to decide who needed one.
One of the things looked at was which medications actually requirerefrigeration by their makers. Insulin in use isn't one of them (including Lantus, per the package insert) . So, WDW told people they no longer would provide refrigerators free of charge for insulin. I've read reports from that time period of people being told by the front desk CMs that insulin did not require refrigeration and if they wanted a fridge, they would either have to pay for it or store the insulin behind the front desk! Even some people who dealt with the Special Reservations people were told the same thing. Definately not a customer friendly attitude.
I don't personally believe anyone should be told by the resort how their medication may be stored. Since insulin is a critical medication, the user needs to be the one deciding how they are comfortable having it stored. Also, since most diabetics I know bring an extra bottle with them (which doesrequire refrigeration per the manufacturer), anyone with insulin who requests a refrigerator needs to be provided with one.
In the past year, I've read more reports of people who got their refrigerator for medication free of charge. So, it does seem to be getting better. If you have a problem with the check in CM, ask to speak to the manager. And check your statement when you check out.
The other hint I have is to check the temperature setting of the refrigerator when you get into the room. We stay at DVC, which has refrigerators in each room. We have frequently found the fridge setting is frequently not set right. When we put water in the fridge, it either stays sort of "just a bit colder than room temp" or it gets a sheet of ice on the top. So, don't assume the temperature is set right (and the duct tape hint is a good idea if you have a portable refrigerator brought into the room).
Duct tape, huh? I'll have to remember that. Glad you caught it before everything ruined. This will be our first long family vacation, so I have not needed to travel and deal with the insulin yet. I'll have to look into getting the cooler that plugs into the cigarette lighter. I imagine it could come in handy for other things too, like baseball tournaments or school field trips. 
